### Introduction

This article presents an engineer's analysis of boat trailer weight distribution performed by Jerry Townsend, a fellow Boston Whaler owner who is a mechanical engineer (M.S.M.E) with considerable experience in modeling of tractor-trailer dynamics. The original motivation for this analysis was a question posed in the Whaler FORUM by John Flook, who was doing some work on his trailer and wanted to know how to predict the tongue weight that would result from movement of the boat or axle position on the trailer. (You can also read the original message thread, Trailer Geometry 101.) Jerry responded with an excellent analysis of the weights and forces involved, and he has since expanded his comments and provided some sketches to supplement his explanations so that they might be more easily understood. The result is the article that appears below.

In addition to solving the tongue weight problem, Professor Townsend also explains a boat weight calculation technique (that had appeared elsewhere but without any derivation of its method) that allows boat weight to be deduced from successive measurements of tongue weight with the boat in different positions on the trailer.

Jerry Townsend was kind enough to write this material and create the illustrations. Jim Hebert converted them into the HTML presentation you see now.

#### by Jerry Townsend

Proper balancing of the loads of your trailer is important to maintain dynamic stability of the vehicle-trailer system. To maintain dynamic stability requires, in part, a recommended hitch load of 5-percent to 10-percent of the towed load. The medium of this range, or 7.5-percent, is considered the target hitch load for our purposes. Changing your boat/trailer load balance can be done experimentally ( i.e., by trial and error) or can be accurately pre-calculated using the method shown below which will result on only a single movement to obtain the desired results.

To understand the forces involved refer to Figure 1 below, which shows the loads of the boat and trailer. The weight of the boat, Wb, is understood to include the weight of the boat, engine, fuel (calculated at about one-half to two-thirds of the fuel capacity) and typical items (such as tools, cooler, etc.) carried in the boat.

After changing your load balance, the center of gravity of the [boat + engine + fuel] will generally be just slightly (perhaps 1-6 inches) in front of the center of the axle(s). Unfortunately when we begin, we normally don't know the location of the center of gravity of the boat + engine + fuel + etc.

 Figure 1. Trailer Hitch Load Model The loads and dimensions of the trailer are shown here Dwg Credit: Jerry Townsend

A first step is to decide how you want to make the correction: by moving the boat or moving the axle(s). Either method can give the desired result. Moving the boat is easier, but you may not want to move the transom away from the end of the trailer. (For information on trailer rigging with regard to proper positioning of the boat on the trailer, see the article on Trailer Rigging.)

In either case, firmly block (using cinder blocks, 4x4's or equivalent equal) the front and back of the wheels on both sides of the trailer to prevent it from moving.

### Experimental Technique

Setting up the boat/trailer balance experimentally is relatively simple and requires knowing the total weight of your [boat + engine + trailer]and the target hitch load (i.e., about 7.5-percent of the total towed weight).

The basic process is to adjust the boat position on the trailer or the location of the axle(s) to give the target hitch load.

We can use a common bathroom scale directly, or if the load is expected to exceed the capacity of the scale, a short piece (about 30 to 40 inches) of 2x6 and a few blocks as shown in Figure 2. The load points on the 2x6 should be as narrow as possible - using a 1" diameter dowel (or equivalent) between the 2x6 and the blocking is good. Using this set-up, the hitch load can be calculated as:

```                           Y3
HitchLoad = WeightScale ( ___ )
Y1
```
 Figure 2. Scale Multiplier Technique The weight measuring capacity of a small scale can be extended using the lever principle. Dwg Credit: Jerry Townsend

#### Moving the Boat

Moving the boat position relative to the trailer can be accomplished by using a come-along (either cable or chain) and other chain/cable/rope as necessary. Do not use nylon rope because, as we all know, nylon rope stretches! In fact, this job is worth purchasing enough plastic encapsulated 3/16" cable and a couple of cable clamps for the task.

You may only need to move the boat an inch or two, so having control of the relative movements is required. Trying to pull the boat with another vehicle will not work. However, a vehicle with its wheels blocked may be used as an anchor for the come-along.

##### Moving Boat Forward

If the hitch load is less than the desired target, the boat must be moved forward via:

1. move the winch standard and boat stop forward to provide at least the desired movement of the boat and then re-tightening the mounting bolts.
2. move the boat forward via the boat winch which may be able to move the boat forward, particularly if the trailer incorporates keel rollers. Should the winch not be sufficient, then use another anchor (tree or vehicle with blocked wheels) as the reference for the come-along.

until the desired target hitch load is achieved. Position the winch standard and boat stop and tighten all bolts.

##### Moving Boat Rearward

If the hitch load is larger than the desired target, the boat must be moved rearward via:

1. connect the come-along to a reference (tree or vehicle with blocked wheels) and connect to the transom anchors. Again, should the trailer incorporate keel rollers, the force required to move the boat can be relatively small.

until the desired target hitch load is achieved. Reposition the winch standard and boat stop and tighten all mounting bolts.

#### Moving the Axles

In the event that you plan on moving the axle(s), consider removing the axle(s), supporting the boat and trailer on jack- stands or automobile frame stands--good solid stuff. Forget the make-do blocking and bumper jacks! The jack-stands make the adjustment process easy because you are able to lower the trailer sufficiently to contact blocking of the trailer frame (rearward from the jack-stands but as close to them as possible so as not to increase the tongue loading excessively). Then move the jack-stands to the desired position, raise the boat/trailer off the frame/transom blocking and determine the hitch loading. Of course, the jack-stands on each trailer rail must be positioned similarly--the same distance from the hitch.

### Analytical Technique

Assume your hitch load needs to be adjusted. How far you would have to move the axle(s) to give the target hitch load? Also assume that a certified scale can be used to determine the weight on the hitch and the weight on the wheels. With this information and the known (or calculated) weight of the [boat + engine + fuel +accessories], you can calculate the location of the center of gravity of the boat and the new position of the boat (or axle) to give the desired hitch load.

Non-engineers don't have to worry so much about the derivation of the formulas; they can just make use of them. It is, however, interesting to see how these equations were derived, which shall be demonstrated below.

A requisite for making the calculations is knowing the location of the center of gravity of the [boat + fuel + engine + accessories]; this itself requires testing and calculations.

The first step in evaluating these loads is to sketch your boat and trailer, as shown in the drawing below, and then to determine the necessary parameters including:

 Wh= Hitch load, lbs Wf= Weight of the frame on the trailer, lbs. This weight must be calculated. We make a few assumptions: we neglect the cross members and assume two rails running the length of the trailer. Many frames are of boxed steel or aluminum sections. Calculate the approximate weight by taking the section size, thickness and length to estimate the weight. Taking a box section of depth, D inches, height of H inches, thickness of t inches, and density of rho, the weight per foot of trailer length becomes: ``` WeightPerFoot = [ (D x H) - (D-2t)(H-2t) ](rho)/144 rho = 490 lb/cu-ft (steel) = 175 lb/cu-ft (aluminum) so that for two box structure rails, and neglecting the cross members, the trailer rail weight, Wf will be: Wf = WeightPerFoot (2) (length of the trailer, ft) ``` Wb= Weight of the boat + engine + fuel + other normally included items (ice cooler, tool box, etc.), lbs. An interesting determination of the boat + engine + etc weight is presented below. Wt= Total weight of the boat (as defined above) and trailer, lbs. If possible, get to a certified scale and independently weigh the load on the tires and the total weight. And, of course, the hitch load is the difference between the total weight and the load on the wheels. If actual weights are not possible, calculate the total weight as close as possible. Remember, gasoline weighs 6.28 lbs/gal and diesel fuel weighs about 6.84 lbs/gal. X1= Distance from the transom to the hitch. X2= Distance from the hitch to the center of the axle(s). X3= Distance from the transom to the center of gravity of the boat. Xf= The length of the trailer frame.

NOTE: All dimensions must be in the same units, inches, feet or whatever.

Notice above that the weight of the trailer frame is identified separately. The reason for this distinction is the trailer frame is centered between the axles and the hitch and therefore is contributing to the hitch load while the wheels, hubs and axles of the trailer are centered at the center of the axle(s). The weight of the tires, wheels, hubs and axle(s) is accounted for as the measured weight on the axle(s).

These parameters will be used via an engineering analysis in which we sum the moments (force times distance) about a given location, defining clockwise as positive. The summation of moments is zero about any pivot point such as the axle(s) or about any free end of a structure such as at the hitch or transom. Note, however that if we sum moments about a point where a force acts, the moment from that force will be zero because the distance of that force to that point is zero. That is, if we sum moments about the hitch, the hitch load is negated in moment formulations. Whereas, if we sum moments about the transom, the hitch load contributes to the moment formulation.

Therefore, we will consider the summation of moment about the transom in accordance with the attached sketch and equate it to zero as:

```Wh(X1) - Wf(X1 - Xf/2) -Wb(X3) + (Wt - Wh)(X1 - X2) = 0     (1)
```

From equation (1), we solve for the location of the center of gravity, X3 as:

```X3 =  Wh(X1) - Wf(X1 - Xf/2) + (Wt - Wh)(X1 - X2)           (2)
_____________________________________________
Wb
```

Knowing the location of the center of gravity of the boat, we then calculate the position of the axle(s), X2, to give the desired hitch load, Wh, as:

```X2 =  Wh(X1) - Wf(X1-Xf/2) - Wb(X3) + (Wt - Wh)X1           (3)
___________________________________________
(Wt - Wh)

```

where the hitch load, Wh, is now the desired hitch load, and the total weight, Wt, is the same as the initial total weight, namely, the initial hitch load plus the initial wheel load.

We have the choice of moving the boat, as modeled by changing the distance X1 as:

```X1 =  Wb(X3) + (Wt - Wh)X2 - Wf(Xf/2)                      (4)
_________________________________
(Wt - Wf)

```

### Real World Example

Now, let's gin up some numbers on the above scenario for an example. Consider the following:

 Wh= Hitch load: 50 lbs (this number is used to illustrate a lower than desired hitch load which would, in all probability, have caused the trailer to be unstable) Wf= Weight of the frame on the trailer: two 21-foot trailer rails each with 6 X 2.5 box steel (490 lbs/cu-ft) with 3/16" walls - giving a calculated weight of :` [6 X 2.5 - (6-3/8)(2.5-3/8)](2 X 490 X 21 / 144) = 435 lbs` Wb= Weight of the boat (1700 lbs), engine (320 lbs), fuel (35 gal @ 6.28 lbs/gal = 220 lbs), and other normally included items (ice cooler, beer, tool box, etc.) (assume 100 lbs) = 2340 lbs Wt= Total weight of the boat (as defined above) and trailer. Assuming the weight of the single axle with tires, wheels and hubs as 150 lbs.:` 2340 + 435 + 150 = 2930 lbs` X1= Distance from the transom to the hitch: 21 ft X2= Distance from the hitch to the center of the axle(s). 17 ft X3= Distance from the transom to the center of gravity of the boat. As calculated below. Xf= Length of the frame: 21 ft

Then, using equation (2) as:

```X3 = Wh(X1) - Wf(X1 - Xf/2) + (Wt - Wh)(X1 - X2)         (2)
___________________________________________
Wb

=  50(21) - 435(21 - 21/2) + (2930 - 50)(21 - 17)
_______________________________________________
2340

=  3.4 ft
```

This is a reasonable number for this example.

Now, let's calculate the location of the axle to give the desired hitch load of (7.5% of 2930 or) 220 lbs. Here we will use equation (3) with the hitch load, Wh, taken as 220 as:

```
X2 = Wh(X1) - Wf(X1-Xf/2) - Wb(X3) + (Wt - Wh)X1         (3)
____________________________________________
(Wt - Wh)

=  (220(21) - 435(21 - 21/2) -2340(3.4) + (2930 - 220)21
______________________________________________________
(2930 - 220)

=  18.1 ft
```

Therefore, in this example, you would want to move the axle back from 17 feet to 18.1 feet from the hitch.

Notice the location of the center of gravity of the boat is 3.4 feet from the transom or 17.6 feet (21 - 3.4) from the hitch. Therefore, the center gravity of the boat is about 6 inches (18.1 ft - 17.6 ft) in front of the center of the axle(s).

Now, what boat movement is necessary should we want to move the boat to give the desired hitch load of 220 lbs. Here, we will use equation (4) as:

```X1 = Wb(X3) + (Wt - Wh)X2 - Wf(Xf/2)                     (4)
_______________________________
Wt - Wf

= 2340(3.4) + (2930 - 220)17 - 435(21/2)
_____________________________________
2930 - 435

= 19.8 ft
```

or move the boat forward 1.2 feet. (21 - 19.8)

Then the center of gravity of the boat + engine + etc. would then be at 16.8 feet (19.8 - 3.4) from the hitch and then about 2.4 inches (17 ft - 16.8 ft) in front of the axle.

### Computer Assistant

To facilitate making all calculations, a DOS executable computer program is available. The program contains instructions for its use.

### Deducing Total Weight From Tongue Weight

Dan Taurone of Metuchen, New Jersey, brought to the attention of the continuousWave FORUM, a technique he noted on the world wide web to weigh a boat + engine + fuel + etc. using a bathroom scale. The method is technically correct as shown below, however the result may not be accurate as there is the potential of amplified errors. Use the method as desired, but be aware of the limitations.

#### Analysis of Bathroom Scale Method

We sum moments about the axle as:

```Wh(X2) - Wf(X2-Xf/2) - Wb[X1-(X1-X3)-(X1-X2)] = 0       (5)

```

and simplifying

```Wh'(X2) - Wf(X2-Xf/2) - Wb(-X1-Y+X3+X2) = 0             (6a)

```

Solving for the common terms `Wf(X2-Xf/2)` in both (5a) and (6a).

```
Wf(X2-Xf/2) = Wh(X2) - Wb(X3+X2-X1)                    (5b)

Wf(X2-Xf/2) = Wh'(X2) - Wb(X3+X2-X1-Y)                 (6b)

```

Equating (5b) and (6b) gives:

```
Wh(X2) - Wb(X3+X2-X1) = Wh'(X2) - Wb(X3+X2-X1-Y)

```

and solving for the weight of the boat/engine/fuel/et.al as:

```
Wb = (Wh - Wh')X2
_____________
Y

```

where:

 Wb= Weight of boat + engine + fuel + etc. Wh= Initial hitch load Wh'= Hitch load with boat displaced X2= Distance from the hitch to the axle Y= Distance the boat displaced Xf= Length of the frame: 21 ft

Which is the method given. Therefore the formulation is correct. One should, however, be cautious because:

1. bathroom scales are not necessarily accurate;
2. the subtraction of two relatively small numbers that may be in error compounds those errors;
3. the error is then amplified many (50 to 200) times by multiplying by the factor X2/Y.

Further, a potential safety or damage concern arises because when displacing the boat, it is possible that the boat center of gravity could be moved rearward of the axle(s) and the boat and trailer would then tip, sending the tongue high.

Jerry Townsend
Idaho Falls, Idaho
March 21, 2001
jtown2354@aol.com

DISCLAIMER: This information is believed to be accurate but there is no guarantee. We do our best!

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